Elasticity-associated rebinding rate of molecular bonds between soft elastic media.

A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix are usually comparable with that of the bonds, making their rebinding events globally coupled with the deformation states of whole systems. Unfortunately, this important principle is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions. In this study, we considered a new theoretical model of a cluster of ligand-receptor bonds between two soft elastic bodies, in which the rebinding rates of ligands to receptors are described, by considering the deformation of the overall system under the influence of bond distributions. On the basis of theory of continuum and statistical mechanics, we obtained an elasticity-associated rebinding rate of open bonds in a closed analytical form that highly depends on the binding states and distributions of all other bonds as well as on the overall deformation energy stored in the elastic bodies and all closed bonds. On the basis of this elasticity-associated rebinding rate and by performing Monte Carlo simulations, we uncovered new mechanisms underlying the adhesion stability of molecular-bond clusters associated with deformable elastic bodies. Moreover, we revealed that the rebinding processes of molecular bonds is not only dependent on interfacial separation but is related to overall energy. This newly proposed rebinding rate may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.

Effects of dynamic radial tensile stress on fibrocartilage differentiation of bone marrow mesenchymal stem cells.

BACKGROUND: Uniaxial/biaxial tensile stress has been employed to induce chondrocyte differentiation of mesenchymal stem cells. However, the effects of radial tensile stimuli on differentiation of MSCs into fibrocartilage remain unclear. RESULTS: It was found that induced bone marrow mesenchymal stem cells (BMSCs) were not only similar to TMJ disc cells in morphology, but also could synthesize type I collagen (Col I), a small amount of type II collagen (Col II) and glycosaminoglycans (GAGs). The synthesis of Col I significantly increased while that of Col II gradually decreased with increasing tensile strength. The ratio of Col I to Col II was 1.8 to 1 and 2 to 1 in the 10% and 15% stretching groups, respectively. The gene expression of Col I and GAGs was significantly upregulated, whereas that of Col II was downregulated. However, the higher tensile stimulation (15%) promoted the synthesis of α-smooth muscle actin (α-SMA). Too much α-SMA is not conducive to constructing engineered tissue. CONCLUSION: Therefore, the 10% radial tensile stimulus was the optimal strength for inducing the BMSCs to differentiate into fibrochondrocytes of the temporomandibular joint (TMJ) disc. This work provided a novel approach for inducing BMSCs to differentiate into fibrochondrocytes.

Mechanical Model for Catch-Bond-Mediated Cell Adhesion in Shear Flow.

Catch bond, whose lifetime increases with applied tensile force, can often mediate rolling adhesion of cells in a hydrodynamic environment. However, the mechanical mechanism governing the kinetics of rolling adhesion of cells through catch-bond under shear flow is not yet clear. In this study, a mechanical model is proposed for catch-bond-mediated cell adhesion in shear flow. The stochastic reaction of bond formation and dissociation is described as a Markovian process, whereas the dynamic motion of cells follows classical analytical mechanics. The steady state of cells significantly depends on the shear rate of flow. The upper and lower critical shear rates required for cell detachment and attachment are extracted, respectively. When the shear rate increases from the lower threshold to the upper threshold, cell rolling became slower and more regular, implying the flow-enhanced adhesion phenomenon. Our results suggest that this flow-enhanced stability of rolling adhesion is attributed to the competition between stochastic reactions of bonds and dynamics of cell rolling, instead of force lengthening the lifetime of catch bonds, thereby challenging the current view in understanding the mechanism behind this flow-enhanced adhesion phenomenon. Moreover, the loading history of flow defining bistability of cell adhesion in shear flow is predicted. These theoretical predictions are verified by Monte Carlo simulations and are related to the experimental observations reported in literature.

Changes in the mechanical properties of human mesenchymal stem cells during differentiation.

A thorough understanding of the changes in mechanical property behind intracellular biophysical and biochemical processes during differentiation of human mesenchymal stem cells (hMSCs) is helpful to direct and enhance the commitment of cells to a particular lineage. In this study, displacement creep of the mesenchymal cell lineages (osteogenic, chondrogenic and adipogenic hMSCs) were determined by using atomic force microscopy, which was then used to determine their mechanical properties. We found that at any stages of differentiation, the mesenchymal cell lineages are linear viscoelastic materials and well matched with a simple power-law creep compliance. In addition, the viscoelasticity of mesenchymal cell lineages showed different trends during differentiation. The adipogenic hMSCs showed continuous softening at all stages. The osteogenic and chondrogenic hMSCs only continuously soften and become more fluid-like in the early stage of differentiation, and get stiffened and less fluid-like in the later stage. These findings will help more accurately imitate cellular biomechanics in the microenvironment, and provided an important reference in the biophysics biomimetic design of stem cell differentiation.

On resistance to virus entry into host cells.

In this article, we adopt a continuum model from Sun and Wirtz (2006. Biophys. J. 90:L10-L12) to show that, for the enveloped virus entry into host cells, the binding energy of the receptor-ligand complex can drive the engulfment of the viral particle to overcome the resistance alternatively dominated by the membrane deformation and cytoskeleton deformation at a different engulfing stage. This is contrary to the conclusions by Sun and Wirtz that the cytoskeleton deformation is always dominant. This discrepancy occurs because the energy of membrane deformation in their article is incorrect. Such an unfortunate small error has led to a severe underestimation of the contribution from membrane deformation to the total energy of the system, which then led them to improperly conclude that the cytoskeleton deformation plays the dominant role in the virus entry into host cell. By using the correct energy expression, our conclusion is justified by energy comparisons under a large range of virus sizes and Young's moduli of cytoskeleton. We even find that a critical radius of virus exists, beyond which the resistance to the virus engulfment becomes dominated by the membrane deformation during the whole stage, contrary to the point of view of Sun and Wirtz.

Anomalous flexural behaviors of microtubules.

Apparent controversies exist on whether the persistence length of microtubules depends on its contour length. This issue is particularly challenging from a theoretical point of view due to the tubular structure and strongly anisotropic material property of microtubules. Here we adopt a higher order continuum orthotropic thin shell model to study the flexural behavior of microtubules. Our model overcomes some key limitations of a recent study based on a simplified anisotropic shell model and results in a closed-form solution for the contour-length-dependent persistence length of microtubules, with predictions in excellent agreement with experimental measurements. By studying the ratio between their contour and persistence lengths, we find that microtubules with length at ~1.5 µm show the lowest flexural rigidity, whereas those with length at ~15 µm show the highest flexural rigidity. This finding may provide an important theoretical basis for understanding the mechanical structure of mitotic spindles during cell division. Further analysis on the buckling of microtubules indicates that the critical buckling load becomes insensitive to the tube length for relatively short microtubules, in drastic contrast to the classical Euler buckling. These rich flexural behaviors of microtubules are of profound implication for many biological functions and biomimetic molecular devices.

Effects of Lipid Deposition on Viscoelastic Response in Human Hepatic Cell Line HepG2.

Hepatic steatosis is associated with various liver diseases. The main pathological feature of steatosis is the excessive lipid accumulation. Ultrasound has been extensively used for the diagnosis of hepatic steatosis. However, most ultrasound-based non-invasive methods are still not accurate enough for cases with light lipid infiltration. One important reason is that the extent to which lipid infiltration may affect mechanical properties of hepatocytes remains unknown. In this work, we used atomic force microscope and in vitro dose-dependent lipid deposition model to detect the quantitative changes of mechanical properties under different degrees of steatosis in a single-cell level. The results show that hepatic cells with lipid deposition can be treated as linear viscoelastic materials with the power law creep compliance and relaxation modulus. Further analysis showed that even slight accumulation of lipid can lead to measurable decrease of stiffness and increased fluidity in liver cells. The accurate detection of viscoelastic properties of hepatocytes and the analysis methods may provide novel insights into hepatic steatosis grading, especially in the very early stage with reversible liver lesion. The application of viscoelasticity index for grading fat deposition might be a new detection indicator in future clinical diagnosis.

Role of Ligand Distribution in the Cytoskeleton-Associated Endocytosis of Ellipsoidal Nanoparticles.

Nanoparticle (NP)-cell interaction mediated by receptor-ligand bonds is a crucial phenomenon in pathology, cellular immunity, and drug delivery systems, and relies strongly on the shape of NPs and the stiffness of the cell. Given this significance, a fundamental question is raised on how the ligand distribution may affect the membrane wrapping of non-spherical NPs under the influence of cytoskeleton deformation. To address this issue, in this work we use a coupled elasticity-diffusion model to systematically investigate the role of ligand distribution in the cytoskeleton-associated endocytosis of ellipsoidal NPs for different NP shapes, sizes, cytoskeleton stiffness, and the initial receptor densities. In this model, we have taken into account the effects of receptor diffusion, receptor-ligand binding, cytoskeleton and membrane deformations, and changes in the configuration entropy of receptors. By solving this model, we find that the uptake process can be significantly influenced by the ligand distribution. Additionally, there exists an optimal state of such a distribution, which corresponds to the fastest uptake efficiency and depends on the NP aspect ratio and cytoskeleton stiffness. We also find that the optimal distribution usually needs local ligand density to be sufficiently high at the large curvature region. Furthermore, the optimal state of NP entry into cells can tolerate slight changes to the corresponding optimal distribution of the ligands. The tolerance to such a change is enhanced as the average receptor density and NP size increase. These results may provide guidelines to control NP-cell interactions and improve the efficiency of target drug delivery systems.

Tuning cellular uptake of nanoparticles via ligand density: Contribution of configurational entropy.

The bioactivity of nanoparticles (NPs) crucially depends on their ability to cross biological membranes. A fundamental understanding of cell-NP interaction is hence essential to improve the performance of the NP-based biomedical applications. Although extensive studies of cellular uptake have converged upon the idea that the uptake process is mainly regulated by the elastic deformation of the cell membrane or NP, recent experimental observations indicate the ligand density as another critical factor in modulating NP uptake into cells. In this study, we propose a theoretical model of the wrapping of an elastic vesicle NP by a finite lipid membrane to depict the relevant energetic and morphological evolutions during the wrapping process driven by forming receptor-ligand bonds. In this model, the deformations of the membrane and the vesicle NP are assumed to follow the continuum Canham-Helfrich framework, whereas the change of configurational entropy of receptors is described from statistical thermodynamics. Results show that the ligand density strongly affects the binding energy and configurational entropy of free receptors, thereby altering the morphology of the vesicle-membrane system in the steady wrapping state. For the wrapping process by the finite lipid membrane, we also find that there exists optimal ligand density for the maximum wrapping degree. These predictions are consistent with relevant experimental observations reported in the literature. We have further observed that there are transitions of various wrapping phases (no wrapping, partial wrapping, and full wrapping) in terms of ligand density, membrane tension, and molecular binding energy. In particular, the ligand and receptor shortage regimes for the small and high ligand density are, respectively, identified. These results may provide guidelines for the rational design of nanocarriers for drug delivery.

Carbon Ion Irradiation Enhances the Anti-tumor Efficiency in Tongue Squamous Cell Carcinoma via Modulating the FAK Signaling.

Oral cancer is a very aggressive disease with high rates of recurrence and metastasis. This study aimed at addressing how efficiently tongue cancer is suppressed after carbon ion irradiation. Here, the close relationship between upregulated expression of focal adhesion kinase (FAK) and high metastatic status in tongue squamous cell carcinoma patients was validated using bioinformatics and immunohistochemical analyses. Our data indicated that FAK suppression significantly enhanced the killing effect induced by irradiation in the tongue cancer cell line CAL27, as evidenced by increased apoptotic induction and reduced colony formation. More importantly, in FAK-deficient cells, carbon ion irradiation was shown to remarkably inhibit migration and invasion by delaying wound healing and slowing down motility. Further studies revealed that irradiation exposure caused disorganization of the actin cytoskeleton and reduced cell adhesive energy in FAK-deficient cells. Moreover, carbon ion treatment, in combination with FAK silencing, markedly blocked the phosphorylation levels of FAK, and paxillin, which partly contributed to the reduced motility of tongue squamous cell carcinoma CAL27 cells. Collectively, these results suggest that the prominent obstructing role of carbon ion irradiation in the growth inhibition and metastatic behavior of tumors, including attenuation of cell adhesiveness, motility, and invasiveness, could be distinctly modulated by FAK-mediated downstream pathways.

Nanomorphological and mechanical reconstruction of mesenchymal stem cells during early apoptosis detected by atomic force microscopy.

Stem cell apoptosis exists widely in embryonic development, tissue regeneration, repair, aging and pathophysiology of disease. The molecular mechanism of stem cell apoptosis has been extensively investigated. However, alterations in biomechanics and nanomorphology have rarely been studied. Therefore, an apoptosis model was established for bone marrow mesenchymal stem cells (BMSCs) and the reconstruction of the mechanical properties and nanomorphology of the cells were investigated in detail. Atomic force microscopy (AFM), scanning electron microscopy (SEM), laser scanning confocal microscopy (LSCM), flow cytometry and Cell Counting Kit-8 analysis were applied to assess the cellular elasticity modulus, geometry, nanomorphology, cell surface ultrastructure, biological viability and early apoptotic signals (phosphatidylserine, PS). The results indicated that the cellular elastic modulus and volume significantly decreased, whereas the cell surface roughness obviously increased during the first 3 h of cytochalasin B (CB) treatment. Moreover, these alterations preceded the exposure of biological apoptotic signal PS. These findings suggested that cellular mechanical damage is connected with the apoptosis of BMSCs, and the alterations in mechanics and nanomorphology may be a sensitive index to detect alterations in cell viability during apoptosis. The results contribute to further understanding of apoptosis from the perspective of cell mechanics.

Lifetime and strength of periodic bond clusters between elastic media under inclined loading.

Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. To understand the mechanical responses of focal adhesions, here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. We first establish a fundamental scaling law of interfacial traction distribution and derive a stress concentration index that governs the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we then perform Monte Carlo simulations to investigate the effects of cluster size, cell/extracellular matrix modulus, and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery and sense mechanical properties of their surroundings.

Stretching Wormlike Chains in Narrow Tubes of Arbitrary Cross-Sections.

We considered the stretching of semiflexible polymer chains confined in narrow tubes with arbitrary cross-sections. Based on the wormlike chain model and technique of normal mode decomposition in statistical physics, we derived a compact analytical expression on the force-confinement-extension relation of the chains. This single formula was generalized to be valid for tube confinements with arbitrary cross-sections. In addition, we extended the generalized bead-rod model for Brownian dynamics simulations of confined polymer chains subjected to force stretching, so that the confinement effects to the chains applied by the tubes with arbitrary cross-sections can be quantitatively taken into account through numerical simulations. Extensive simulation examples on the wormlike chains confined in tubes of various shapes quantitatively justified the theoretically derived generalized formula on the force-confinement-extension relation of the chains.

Statistical Behaviors of Semiflexible Polymer Chains Stretched in Rectangular Tubes.

We investigated the statistical behaviors of semiflexible polymer chains, which were simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by using which new compact formulas were obtained for the confinement free energy and force⁻confinement⁻extension relations. These newly derived formulas were justified by numerical solutions of the eigenvalue problem associated with the Fokker⁻Planck governing equation and extensive Brownian dynamics simulations based on the so-called generalized bead-rod (GBR) model. We found that, compared to classical deflection theory, these new formulas were valid for a much more extended range of the confinement size/persistence length ratio and had no adjustable fitting parameters for sufficiently long semiflexible chains in the whole deflection regime.

Mechanical, nanomorphological and biological reconstruction of early­stage apoptosis in HeLa cells induced by cytochalasin B.

There is a growing interest in the fact that mechanical signals may be as important as biological signals in evaluating cell viability. To investigate the alterations in biomechanics, nanomorphology and biological apoptotic signals during early apoptosis, an apoptosis model was established for cervical cancer HeLa cells induced by cytochalasin B (CB). The cellular mechanical properties, geometry, morphology and expression of key apoptotic proteins were systematically analyzed. The findings indicated a marked decline in cellular elastic modulus and volume and a considerable increase in surface roughness occurring prior to the activation of biological apoptosis signals (such as phosphatidylserine exposure or activation of CD95/Fas). Moreover, the depolymerization of filamentous actin aggravated the intracellular crowding degree, which induced the redistribution of different­sized protein molecules and protrusions across the cell membrane arising from excluded volume interactions. Statistical analysis revealed that the disassembly of the actin cytoskeleton was negatively correlated with the cellular elastic modulus and volume, but was positively correlated with surface roughness and CD95/Fas activation. The results of the present study suggest that compared with biological signals, mechanical and geometrical reconstruction is more sensitive during apoptosis and the increase in cell surface roughness arises from the redistribution of biophysical molecules. These results contribute to our in­depth understanding of the apoptosis mechanisms of cancer cells mediated by cytochalasin B.

Size and shape effects on diffusion and absorption of colloidal particles near a partially absorbing sphere: implications for uptake of nanoparticles in animal cells.

A mechanics model describing how a cell membrane with diffusive mobile receptors wraps around a ligand-coated cylindrical or spherical particle has been recently developed to model the role of particle size in receptor-mediated endocytosis. The results show that particles in the size range of tens to hundreds of nanometers can enter cells even in the absence of clathrin or caveolin coats. Here we report further progress on modeling the effects of size and shape in diffusion, interaction, and absorption of finite-sized colloidal particles near a partially absorbing sphere. Our analysis indicates that, from the diffusion and interaction point of view, there exists an optimal hydrodynamic size of particles, typically in the nanometer regime, for the maximum rate of particle absorption. Such optimal size arises as a result of balance between the diffusion constant of the particles and the interaction energy between the particles and the absorbing sphere relative to the thermal energy. Particles with a smaller hydrodynamic radius have larger diffusion constant but weaker interaction with the sphere while larger particles have smaller diffusion constant but stronger interaction with the sphere. Since the hydrodynamic radius is also determined by the particle shape, an optimal hydrodynamic radius implies an optimal size as well as an optimal aspect ratio for a nonspherical particle. These results show broad agreement with experimental observations and may have general implications on interaction between nanoparticles and animal cells.

Effects of ligand distribution on receptor-diffusion-mediated cellular uptake of nanoparticles.

Biophysical-factor-dependent cellular uptake of nanoparticles (NPs) through receptor-diffusion-mediated endocytosis bears significance in pathology, cellular immunity and drug-delivery systems. Advanced nanotechnology of NP synthesis provides methods for modifying NP surface with different ligand distributions. However, no report discusses effects of ligand distribution on NP surface on receptor-diffusion-mediated cellular uptake. In this article, we used a statistical dynamics model of receptor-diffusion-mediated endocytosis to examine ligand-distribution-dependent cellular uptake dynamics by considering that ligand-receptor complexes drive engulfing to overcome resistance to membrane deformation and changes in configuration entropy of receptors. Results showed that cellular internalization of NPs strongly depended on ligand distribution and that cellular-uptake efficiency of NPs was high when ligand distribution was within a range around uniform distribution. This feature of endocytosis ensures robust infection ability of viruses to enter host cells. Interestingly, results also indicated that optimal ligand distribution associated with highest cellular-uptake efficiency slightly depends on distribution pattern of ligands and density of receptors, and the optimal distribution becomes uniform when receptor density is sufficiently large. Position of initial contact point is also a factor affecting dynamic wrapping. This study explains why most enveloped viruses present almost homogeneous ligand distribution and is useful in designing controlled-release drug-delivery systems.

Stretching a Semiflexible Polymer in a Tube.

How the statistical behavior of semiflexible polymer chains may be affected by force stretching and tube confinement is a classical unsolved problem in polymer physics. Based on the Odijk deflection theory and normal mode decomposition in terms of Fourier expansion, we have derived a new compact formula for the extension of a wormlike chain of finite length strongly confined in a tube and simultaneously stretched by an external force. We have also suggested a new deflection length, which together with the force-extension relation is valid for a very extended range of the tube-diameter/persistence-length ratio comparing to the classic Odijk theory. The newly derived formula has no adjustable fitting parameters for the whole deflection regime; in contrast, the classic Odijk length needs different prefactors to fit the free energy and average extension, respectively. Brownian dynamics simulations based on the Generalized Bead-Rod (GBR) model were extensively performed, which justified the theoretical predictions.

A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion.

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand-receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

Carbon Ion-Irradiated Hepatoma Cells Exhibit Coupling Interplay between Apoptotic Signaling and Morphological and Mechanical Remodeling.

A apoptotic model was established based on the results of five hepatocellular carcinoma cell (HCC) lines irradiated with carbon ions to investigate the coupling interplay between apoptotic signaling and morphological and mechanical cellular remodeling. The expression levels of key apoptotic proteins and the changes in morphological characteristics and mechanical properties were systematically examined in the irradiated HCC lines. We observed that caspase-3 was activated and that the Bax/Bcl-2 ratio was significantly increased over time. Cellular morphology and mechanics analyses indicated monotonic decreases in spatial sizes, an increase in surface roughness, a considerable reduction in stiffness, and disassembly of the cytoskeletal architecture. A theoretical model of apoptosis revealed that mechanical changes in cells induce the characteristic cellular budding of apoptotic bodies. Statistical analysis indicated that the projected area, stiffness, and cytoskeletal density of the irradiated cells were positively correlated, whereas stiffness and caspase-3 expression were negatively correlated, suggesting a tight coupling interplay between the cellular structures, mechanical properties, and apoptotic protein levels. These results help to clarify a novel arbitration mechanism of cellular demise induced by carbon ions. This biomechanics strategy for evaluating apoptosis contributes to our understanding of cancer-killing mechanisms in the context of carbon ion radiotherapy.